Problem: Simplify the following expression: $k = \dfrac{8}{a + 5} \div \dfrac{6}{10a}$
Dividing by an expression is the same as multiplying by its inverse. $k = \dfrac{8}{a + 5} \times \dfrac{10a}{6}$ When multiplying fractions, we multiply the numerators and the denominators. $k = \dfrac{ 8 \times 10a } { (a + 5) \times 6}$ $k = \dfrac{80a}{6a + 30}$ Simplify: $k = \dfrac{40a}{3a + 15}$